Solve for $x$ and $y$ using elimination. ${2x-4y = -16}$ ${-3x-3y = -30}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $-4$ ${6x-12y = -48}$ $12x+12y = 120$ Add the top and bottom equations together. $18x = 72$ $\dfrac{18x}{{18}} = \dfrac{72}{{18}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {2x-4y = -16}\thinspace$ to find $y$ ${2}{(4)}{ - 4y = -16}$ $8-4y = -16$ $8{-8} - 4y = -16{-8}$ $-4y = -24$ $\dfrac{-4y}{{-4}} = \dfrac{-24}{{-4}}$ ${y = 6}$ You can also plug ${x = 4}$ into $\thinspace {-3x-3y = -30}\thinspace$ and get the same answer for $y$ : ${-3}{(4)}{ - 3y = -30}$ ${y = 6}$